The thermal power radiated by a black body is given by Stefan's law, according to which the power radiated (P) is directly proportional to the fourth power of the absolute temperature
(T) of the body. This can be mathematically expressed as:
P=σeAT4where:
σ is the Stefan-Boltzmann constant,
e is the emissivity of the surface,
A is the surface area,
T is the absolute temperature in Kelvin.
For the given problem, since both black bodies have equal surface areas and are perfect black bodies (assuming
e=1 for both), the ratio of their thermal powers
PP to
PQ can be simplified to the ratio of the fourth powers of their absolute temperatures. To work with absolute temperatures, we must first convert the given Celsius temperatures to Kelvin:
Temperature of
P=127∘C=127+273=400KTemperature of
Q=27∘C=27+273=300K The ratio of their thermal powers can thus be expressed as:
‌=‌| σ×A×(400)4 |
| σ×A×(300)4 |
Simplifying this, we get:
‌=‌=(‌)4Calculating the power of 4 :
‌=(‌)=‌Therefore, the correct option is:
Option D
256:81.